Didactic calculus modules and the learning of definite integrals in engineering students at a Peruvian public university

Abstract

Didactic modules are autonomous and structured learning units that logically organize theoretical content, practical activities, and evaluation processes. This research evaluated the influence of didactic modules on the learning of definite integrals among Systems Engineering students at the National University of the Altiplano. Faced with persistent difficulties in conceptual understanding and the predominance of mechanical teaching, a quantitative approach was applied with a pre-experimental design of pretest and posttest to a sample of 23 students through non-probabilistic convenience sampling, using a non-parametric Wilcoxon test. The results showed a significant improvement in academic performance, with an increase in the overall mean from 9.13 to 12.48. Initially, 78.3% of the students were at the "Beginning" level; after the intervention, this percentage decreased to 21.7%, shifting most students to the "Process" and "Achievement" levels. The greatest impact was observed in the dimension of the Fundamental Theorem of Calculus, where the gap between differentiation and integration was closed. Likewise, didactic mediation facilitated the transition from the geometric interpretation of Riemann sums to the analytical formalization of the limit. It is concluded that the use of pedagogically structured modules is an effective strategy to overcome cognitive barriers, promoting meaningful learning and better internalization of operational properties in integral calculus.